Exercise 3
Yuting Huang, Jipeng Cheng, Weidi Hou
4/5/2022
Problem 1: What causes what?
Question 1. Why can’t I just get data from a few different cities and run the regression of “Crime” on “Police” to understand how more cops in the streets affect crime? (“Crime” refers to some measure of crime rate and “Police” measures the number of cops in a city.)
answer: In this question of “Crime” and “Police”, there is a problem of endogeneity circle. if we use the simple linear regresstion model \[y=beta_1+beta_2 * x+u\], there is a problem of endogeneity, i.e. E(xu)≠0. Under is circumstance, inconsistency of OLS arises due to the fact that changes in x(police force) are associated not only with chages in y(crime), but also change in u.
Question2. How were the researchers from UPenn able to isolate this effect? Briefly describe their approach and discuss their result in the “Table 2” below, from the researchers’ paper.
answer: In the paper, the authors use a “high-alert periods” dummy variable to break the circle of endogeneity to estimate the effect of police on crime. The reason why the authors choose “high-alert periods” is that the primary purpose of the HSAS is to inform and coordinate the antiterrorism efforts of all federal agencies. So, it the level of alert will directly impact the number of police on the specific district. In addition, the authors use daily data to make sure the “treatment windows” are short. Plus, the choosing data includes the information repeated terror alert, so it reduces the possibility of spurious correlation. Furthermore, the model also uses a “Metro ridership” variable to test whether there is a correlation between tourism and crime. At last, the authors use dummy variables for each day of the week to control for day effects.
From the Table 2 column 1, the coefficient on the alert level is statistically significant at the 5 percent level and indicates that on high-alert days, total crimes decrease by an average of seven crimes per day, or approximately 6.6 percent. From the Table 2 column 2, we verify that high-alert levels are not being confounded with tourism levels by including logged midday Metro ridership directly in the regression. The coefficient on the alert level is slightly smaller, at -6.2 crimes per day. We also find that increased Metro ridership is correlated with an increase in crime. The increase, however, is very small, a 10 percent increase in Metro ridership increases the number of crimes by only 1.7 per day on average. Thus, given that midday Metro ridership is a good proxy for tourism, changes in the number of tourists cannot explain the systematic change in crime that we estimate.
Question3. Why did they have to control for Metro ridership? What was that trying to capture?
In order to test a hypothesis that tourism is reduced on high-alert days, and as a result, there are fewer potential victims, which leads to fewer crimes.
Question4. Below I am showing you “Table 4” from the researchers’ paper. Just focus on the first column of the table. Can you describe the model being estimated here? What is the conclusion?
The model in table 4 includes district fixed effects in order to distinguish the peculiar crime pattern of each district, and all regressions contain day-of-the-week fixed effects. The dependent variable is daily crime totals by district. From Table 4, During periods of high alert, crime in the National Mall area decreases by 2.62 crimes per day. Crime also decreases in the other districts, by 0.571 crimes per day, but this effect is not statistically significant. Since there are 17.1 crimes on the district 1, the declination during high-alert days is approximately 15 percent, which means almost one-half of the total crime decline during high-alert periods is concentrated in District 1. In addition, The result elasticity of crime with respect to police is -0.3, which is consistent with other researchers’ results.
Problem 2: Tree modeling: dengue cases
## Distribution not specified, assuming gaussian ...## [,1] [,2] [,3]
## [1,] 40.25508 38.33396 37.5778Use Kable to name columns in .Rmd. The results suggest that random forests mode have the best performance on the testing data.
Problem 3: Predictive model building: green certification
Overview
As landlords and renters, what they mostly care about is their possible revenue per square foot per calendar year. As we all know, their revenue depends on many factors, such as the age, facilities, amenities , leasing rate and so on. Nowadays, people pay more attention on their living environment when renting a house, such as whether this landload has a green certification. Therefore, it’s meaningful to do some research on the relationship between rental income and green certification.
In our report, we build our best predictive model possible for revenue per square foot per calendar year and to use this model to quantify the average change in rental income per square foot associated with green certification, holding other features of the building constant.
Data and research design
Data
In our raw data set, there are 7,894 data points. We first filter out those missing data. Now, our new greenbuildings data set has 7820 data points.
predictive variable and features
The predictive variable is revenue per square foot per year, which is the product of two terms: rent and leasing_rate.
The features used to build our model are:
(1) CS.PropertyID: the building's unique identifier in the database.
(2) cluster: an identifier for the building cluster, with each cluster containing one green-certified building and at least one other non-green-certified building within a quarter-mile radius of the cluster center.
(3) size: the total square footage of available rental space in the building.
(4) empl.gr: the year-on-year growth rate in employment in the building's geographic region.
(5) Rent: the rent charged to tenants in the building, in dollars per square foot per calendar year.
(6) leasing.rate: a measure of occupancy; the fraction of the building's available space currently under lease.
(7) stories: the height of the building in stories.
(8) age: the age of the building in years.
(9) renovated: whether the building has undergone substantial renovations during its lifetime.
(10) (11) class.a, class.b: indicators for two classes of building quality (the third is Class C). These are relative classifications within a specific market. Class A buildings are generally the highest-quality properties in a given market. Class B buildings are a notch down, but still of reasonable quality. Class C buildings are the least desirable properties in a given market.
(12) green.rating: an indicator for whether the building is either LEED- or EnergyStar-certified.
(13) LEED, Energystar: indicators for the two specific kinds of green certifications.
(14) net: an indicator as to whether the rent is quoted on a "net contract" basis. Tenants with net-rental contracts pay their own utility costs, which are otherwise included in the quoted rental price.
(15) amenities: an indicator of whether at least one of the following amenities is available on-site: bank, convenience store, dry cleaner, restaurant, retail shops, fitness center.
(16) cd.total.07: number of cooling degree days in the building's region in 2007. A degree day is a measure of demand for energy; higher values mean greater demand. Cooling degree days are measured relative to a baseline outdoor temperature, below which a building needs no cooling.
(17) hd.total07: number of heating degree days in the building's region in 2007. Heating degree days are also measured relative to a baseline outdoor temperature, above which a building needs no heating.
(18) total.dd.07: the total number of degree days (either heating or cooling) in the building's region in 2007.
(19) Precipitation: annual precipitation in inches in the building's geographic region.
(20) Gas.Costs: a measure of how much natural gas costs in the building's geographic region.
(21)Electricity.Costs: a measure of how much electricity costs in the building's geographic region.
(22)City_Market_Rent: a measure of average rent per square-foot per calendar year in the building's local market.research design
By using the tree model to build our predictive model, we identify the association between rental revenue and green certification. We first split the new greenbuilds data set into training and test test, then we use two different tree methods: random forest and boosted regression trees to build our model. Then we calculate the out of sample RMSE. The result shows that the RMSE of the random forest model is lower that the one using boosted regression trees. Therefore, we choose to use random forest method.
Results
Figure 1: Figure of all features used in our predictive model descending by importance.
From Figure 1, we found that the most important features that landlords should consider are “size, age, stories”, these variables seems to be the most important. However, the “green_rating” variable is not that important from our observation.
Figure 2: Impact of Green Certifications on Revenue
From the box plot including the information between revenue and green_rating, the average rent per square foot is around 20 for buildings with a green certification, and around 24 for those without a certification. Therefore, we didn’t find significant difference between buildings with or without green certification.
## # A tibble: 2 × 2
## green_rating `mean(predict_rent)`
## <int> <dbl>
## 1 0 23.3
## 2 1 25.3Table 1: The average change in revenue per square foot related to green certification
We then calculate the average change in revenue per square foot for buildings with or without green certification. From the table above, we found that buildings with green certification get more revenue than those without green certification, but the impact is small, considering the difference is 2 unit.
Figure 3: Partial Effect of Green Certifications on Revenue
From the partial effect figure of green certification on revenue per square foot, we found a positive association between revenue and green certification, which means green certification has some good impact on revenue.
Conclusion
From our analysis, we build the model using random forest to estimate the association between green certification and revenue per square foot. From our results, we found that green certification has some positive impact on revenue, but the impact isn’t very significant. In addition, we found that these variables “size, age, stories” have more impact on revenue. Based on our research, the landlords should weigh the pros and cons of getting a green certification, thinking critically about the cost and revenue change of getting a green certification. If they figure that the income change isn’t overweigh the cost of getting a certification, they should focus on other features, which have more important impact on revenue.
Problem 4: Predictive model building: California housing
Our purpose is to build the best predictive model to forecast the median house value in California. According to the topic description, in the beginning, we have to conduct standardized processing for “totalRooms” and totalBedrooms" by creating the new variables including “sdrooms” and “sdbedrooms”. Then we utilized three different methods including Step wise, Random Forecast and boost, to build the best predictive model.
## longitude latitude housingMedianAge totalRooms totalBedrooms population
## 1 -122.23 37.88 41 880 129 322
## 2 -122.22 37.86 21 7099 1106 2401
## 3 -122.24 37.85 52 1467 190 496
## 4 -122.25 37.85 52 1274 235 558
## 5 -122.25 37.85 52 1627 280 565
## 6 -122.25 37.85 52 919 213 413
## households medianIncome medianHouseValue
## 1 126 8.3252 452600
## 2 1138 8.3014 358500
## 3 177 7.2574 352100
## 4 219 5.6431 341300
## 5 259 3.8462 342200
## 6 193 4.0368 269700##
## Call:
## lm(formula = medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome, data = cahousing_train)
##
## Coefficients:
## (Intercept) longitude latitude housingMedianAge
## -3.848e+06 -4.517e+04 -4.382e+04 9.431e+02
## sdrooms sdbedrooms population medianIncome
## -1.118e+04 7.472e+04 -5.071e-01 4.338e+04## Start: AIC=323508.1
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome
##
## Df Sum of Sq RSS AIC
## + sdbedrooms:population 1 4.3080e+11 7.6190e+13 323429
## + housingMedianAge:medianIncome 1 1.9125e+11 7.6429e+13 323474
## + latitude:medianIncome 1 1.2638e+11 7.6494e+13 323486
## + population:medianIncome 1 1.2216e+11 7.6498e+13 323487
## + longitude:housingMedianAge 1 6.2305e+10 7.6558e+13 323498
## + sdrooms:medianIncome 1 4.3832e+10 7.6577e+13 323502
## + latitude:sdrooms 1 3.3864e+10 7.6587e+13 323504
## + latitude:housingMedianAge 1 2.4227e+10 7.6596e+13 323505
## + latitude:population 1 2.3524e+10 7.6597e+13 323506
## + housingMedianAge:sdbedrooms 1 2.2179e+10 7.6598e+13 323506
## + longitude:population 1 2.1234e+10 7.6599e+13 323506
## + sdbedrooms:medianIncome 1 1.7614e+10 7.6603e+13 323507
## + longitude:medianIncome 1 1.7590e+10 7.6603e+13 323507
## - population 1 4.1512e+09 7.6625e+13 323507
## <none> 7.6620e+13 323508
## + latitude:sdbedrooms 1 3.2244e+09 7.6617e+13 323509
## + longitude:latitude 1 1.1564e+09 7.6619e+13 323510
## + longitude:sdrooms 1 1.0675e+09 7.6619e+13 323510
## + housingMedianAge:sdrooms 1 2.9511e+08 7.6620e+13 323510
## + housingMedianAge:population 1 2.5704e+08 7.6620e+13 323510
## + sdrooms:population 1 1.3558e+08 7.6620e+13 323510
## + sdrooms:sdbedrooms 1 1.2594e+08 7.6620e+13 323510
## + longitude:sdbedrooms 1 8.6979e+05 7.6620e+13 323510
## - sdrooms 1 1.3380e+12 7.7958e+13 323756
## - housingMedianAge 1 1.6454e+12 7.8266e+13 323813
## - sdbedrooms 1 2.3230e+12 7.8943e+13 323938
## - longitude 1 1.3277e+13 8.9898e+13 325815
## - latitude 1 1.3667e+13 9.0287e+13 325877
## - medianIncome 1 3.9738e+13 1.1636e+14 329542
##
## Step: AIC=323428.6
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population
##
## Df Sum of Sq RSS AIC
## + latitude:sdrooms 1 1.8886e+11 7.6001e+13 323395
## + housingMedianAge:medianIncome 1 1.7761e+11 7.6012e+13 323397
## + latitude:medianIncome 1 1.3547e+11 7.6054e+13 323405
## + population:medianIncome 1 1.3260e+11 7.6057e+13 323405
## + sdrooms:population 1 1.2931e+11 7.6060e+13 323406
## + sdrooms:medianIncome 1 1.0517e+11 7.6084e+13 323411
## + sdrooms:sdbedrooms 1 8.6660e+10 7.6103e+13 323414
## + housingMedianAge:sdbedrooms 1 6.7183e+10 7.6122e+13 323418
## + latitude:sdbedrooms 1 4.9970e+10 7.6140e+13 323421
## + latitude:housingMedianAge 1 4.4800e+10 7.6145e+13 323422
## + longitude:population 1 3.7422e+10 7.6152e+13 323424
## + longitude:housingMedianAge 1 3.0431e+10 7.6159e+13 323425
## + longitude:sdrooms 1 2.9937e+10 7.6160e+13 323425
## + latitude:population 1 2.6978e+10 7.6163e+13 323425
## + longitude:sdbedrooms 1 2.5004e+10 7.6165e+13 323426
## + longitude:medianIncome 1 2.1404e+10 7.6168e+13 323427
## <none> 7.6190e+13 323429
## + housingMedianAge:sdrooms 1 6.5841e+09 7.6183e+13 323429
## + housingMedianAge:population 1 6.0009e+09 7.6184e+13 323429
## + longitude:latitude 1 2.4236e+09 7.6187e+13 323430
## + sdbedrooms:medianIncome 1 4.3275e+07 7.6190e+13 323431
## - sdbedrooms:population 1 4.3080e+11 7.6620e+13 323508
## - sdrooms 1 1.2040e+12 7.7394e+13 323653
## - housingMedianAge 1 1.7732e+12 7.7963e+13 323759
## - longitude 1 1.3647e+13 8.9836e+13 325807
## - latitude 1 1.4016e+13 9.0205e+13 325866
## - medianIncome 1 3.9625e+13 1.1581e+14 329477
##
## Step: AIC=323394.8
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms
##
## Df Sum of Sq RSS AIC
## + latitude:medianIncome 1 3.0250e+11 7.5698e+13 323339
## + longitude:sdrooms 1 1.8861e+11 7.5812e+13 323361
## + population:medianIncome 1 1.6112e+11 7.5840e+13 323366
## + housingMedianAge:medianIncome 1 1.6098e+11 7.5840e+13 323366
## + sdrooms:medianIncome 1 1.0004e+11 7.5901e+13 323378
## + longitude:medianIncome 1 9.0465e+10 7.5910e+13 323380
## + sdrooms:population 1 8.0749e+10 7.5920e+13 323381
## + longitude:housingMedianAge 1 5.9194e+10 7.5942e+13 323385
## + longitude:population 1 4.8497e+10 7.5952e+13 323388
## + latitude:sdbedrooms 1 4.6923e+10 7.5954e+13 323388
## + longitude:sdbedrooms 1 3.8208e+10 7.5963e+13 323389
## + housingMedianAge:sdbedrooms 1 3.7941e+10 7.5963e+13 323390
## + latitude:population 1 3.6427e+10 7.5964e+13 323390
## + sdrooms:sdbedrooms 1 3.4137e+10 7.5967e+13 323390
## + latitude:housingMedianAge 1 2.0609e+10 7.5980e+13 323393
## <none> 7.6001e+13 323395
## + housingMedianAge:population 1 4.5795e+09 7.5996e+13 323396
## + housingMedianAge:sdrooms 1 1.1066e+09 7.6000e+13 323397
## + longitude:latitude 1 7.1494e+08 7.6000e+13 323397
## + sdbedrooms:medianIncome 1 1.7544e+08 7.6001e+13 323397
## - latitude:sdrooms 1 1.8886e+11 7.6190e+13 323429
## - sdbedrooms:population 1 5.8580e+11 7.6587e+13 323504
## - housingMedianAge 1 1.7479e+12 7.7749e+13 323721
## - longitude 1 1.3549e+13 8.9550e+13 325763
## - medianIncome 1 3.9624e+13 1.1562e+14 329455
##
## Step: AIC=323339.1
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome
##
## Df Sum of Sq RSS AIC
## + latitude:sdbedrooms 1 5.1691e+11 7.5181e+13 323242
## + longitude:medianIncome 1 4.9519e+11 7.5203e+13 323246
## + longitude:sdbedrooms 1 2.8451e+11 7.5414e+13 323287
## + housingMedianAge:medianIncome 1 1.8087e+11 7.5517e+13 323307
## + longitude:sdrooms 1 1.4381e+11 7.5554e+13 323314
## + population:medianIncome 1 1.2149e+11 7.5577e+13 323318
## + sdrooms:population 1 8.9177e+10 7.5609e+13 323324
## + sdrooms:medianIncome 1 8.4084e+10 7.5614e+13 323325
## + longitude:population 1 6.2818e+10 7.5635e+13 323329
## + latitude:population 1 5.1393e+10 7.5647e+13 323331
## + longitude:housingMedianAge 1 4.4003e+10 7.5654e+13 323333
## + latitude:housingMedianAge 1 3.8575e+10 7.5660e+13 323334
## + housingMedianAge:sdbedrooms 1 2.0584e+10 7.5678e+13 323337
## + sdrooms:sdbedrooms 1 1.6147e+10 7.5682e+13 323338
## <none> 7.5698e+13 323339
## + housingMedianAge:population 1 7.2100e+09 7.5691e+13 323340
## + longitude:latitude 1 4.8583e+09 7.5693e+13 323340
## + sdbedrooms:medianIncome 1 2.1631e+09 7.5696e+13 323341
## + housingMedianAge:sdrooms 1 1.0106e+07 7.5698e+13 323341
## - latitude:medianIncome 1 3.0250e+11 7.6001e+13 323395
## - latitude:sdrooms 1 3.5589e+11 7.6054e+13 323405
## - sdbedrooms:population 1 6.9851e+11 7.6397e+13 323470
## - housingMedianAge 1 1.6907e+12 7.7389e+13 323656
## - longitude 1 1.3808e+13 8.9506e+13 325758
##
## Step: AIC=323242.1
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms
##
## Df Sum of Sq RSS AIC
## + longitude:medianIncome 1 5.1475e+11 7.4667e+13 323145
## + housingMedianAge:medianIncome 1 1.6864e+11 7.5013e+13 323212
## + population:medianIncome 1 1.3750e+11 7.5044e+13 323218
## + sdrooms:medianIncome 1 8.9918e+10 7.5091e+13 323227
## + longitude:sdrooms 1 6.7080e+10 7.5114e+13 323231
## + longitude:housingMedianAge 1 6.0584e+10 7.5121e+13 323232
## + longitude:population 1 4.7023e+10 7.5134e+13 323235
## + latitude:population 1 4.0162e+10 7.5141e+13 323236
## + sdrooms:population 1 2.9235e+10 7.5152e+13 323239
## + latitude:housingMedianAge 1 2.8850e+10 7.5152e+13 323239
## + housingMedianAge:sdbedrooms 1 1.1626e+10 7.5170e+13 323242
## <none> 7.5181e+13 323242
## + longitude:latitude 1 7.5977e+09 7.5174e+13 323243
## + housingMedianAge:population 1 2.5540e+09 7.5179e+13 323244
## + sdbedrooms:medianIncome 1 2.4872e+09 7.5179e+13 323244
## + longitude:sdbedrooms 1 1.0399e+09 7.5180e+13 323244
## + sdrooms:sdbedrooms 1 4.5599e+08 7.5181e+13 323244
## + housingMedianAge:sdrooms 1 3.7197e+08 7.5181e+13 323244
## - sdbedrooms:population 1 4.9325e+11 7.5675e+13 323335
## - latitude:sdbedrooms 1 5.1691e+11 7.5698e+13 323339
## - latitude:medianIncome 1 7.7249e+11 7.5954e+13 323388
## - latitude:sdrooms 1 8.3348e+11 7.6015e+13 323399
## - housingMedianAge 1 1.6684e+12 7.6850e+13 323557
## - longitude 1 1.4189e+13 8.9371e+13 325738
##
## Step: AIC=323144.9
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome
##
## Df Sum of Sq RSS AIC
## + longitude:sdrooms 1 1.8891e+11 7.4478e+13 323110
## + population:medianIncome 1 1.4776e+11 7.4519e+13 323118
## + housingMedianAge:medianIncome 1 8.3075e+10 7.4584e+13 323131
## + sdrooms:medianIncome 1 7.3397e+10 7.4593e+13 323133
## + longitude:housingMedianAge 1 6.7796e+10 7.4599e+13 323134
## + sdbedrooms:medianIncome 1 5.3271e+10 7.4613e+13 323137
## + longitude:population 1 4.9687e+10 7.4617e+13 323137
## + latitude:population 1 4.6961e+10 7.4620e+13 323138
## + latitude:housingMedianAge 1 4.1984e+10 7.4625e+13 323139
## + housingMedianAge:sdrooms 1 2.6294e+10 7.4640e+13 323142
## + sdrooms:population 1 2.2949e+10 7.4644e+13 323142
## + longitude:latitude 1 1.0909e+10 7.4656e+13 323145
## <none> 7.4667e+13 323145
## + housingMedianAge:sdbedrooms 1 2.7477e+09 7.4664e+13 323146
## + housingMedianAge:population 1 2.2276e+09 7.4664e+13 323146
## + sdrooms:sdbedrooms 1 8.5795e+08 7.4666e+13 323147
## + longitude:sdbedrooms 1 4.7749e+08 7.4666e+13 323147
## - sdbedrooms:population 1 4.9162e+11 7.5158e+13 323238
## - longitude:medianIncome 1 5.1475e+11 7.5181e+13 323242
## - latitude:sdbedrooms 1 5.3648e+11 7.5203e+13 323246
## - latitude:sdrooms 1 8.7124e+11 7.5538e+13 323310
## - latitude:medianIncome 1 1.0060e+12 7.5673e+13 323336
## - housingMedianAge 1 1.5033e+12 7.6170e+13 323431
##
## Step: AIC=323110.3
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms
##
## Df Sum of Sq RSS AIC
## + longitude:sdbedrooms 1 7.1904e+11 7.3759e+13 322972
## + population:medianIncome 1 1.6167e+11 7.4316e+13 323081
## + sdbedrooms:medianIncome 1 8.7856e+10 7.4390e+13 323095
## + housingMedianAge:medianIncome 1 8.0195e+10 7.4397e+13 323097
## + longitude:housingMedianAge 1 5.2347e+10 7.4425e+13 323102
## + latitude:housingMedianAge 1 5.0157e+10 7.4428e+13 323103
## + longitude:population 1 4.1963e+10 7.4436e+13 323104
## + latitude:population 1 4.1401e+10 7.4436e+13 323104
## + sdrooms:medianIncome 1 4.0787e+10 7.4437e+13 323104
## + sdrooms:sdbedrooms 1 3.2926e+10 7.4445e+13 323106
## + housingMedianAge:sdrooms 1 1.3701e+10 7.4464e+13 323110
## + sdrooms:population 1 1.0692e+10 7.4467e+13 323110
## <none> 7.4478e+13 323110
## + housingMedianAge:sdbedrooms 1 7.6239e+09 7.4470e+13 323111
## + longitude:latitude 1 6.5444e+09 7.4471e+13 323111
## + housingMedianAge:population 1 1.9268e+09 7.4476e+13 323112
## - longitude:sdrooms 1 1.8891e+11 7.4667e+13 323145
## - latitude:sdbedrooms 1 4.1766e+11 7.4895e+13 323189
## - sdbedrooms:population 1 6.0883e+11 7.5087e+13 323226
## - longitude:medianIncome 1 6.3658e+11 7.5114e+13 323231
## - latitude:sdrooms 1 1.0372e+12 7.5515e+13 323308
## - latitude:medianIncome 1 1.1097e+12 7.5587e+13 323322
## - housingMedianAge 1 1.4144e+12 7.5892e+13 323380
##
## Step: AIC=322972.1
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms
##
## Df Sum of Sq RSS AIC
## + population:medianIncome 1 1.9111e+11 7.3568e+13 322937
## + sdrooms:sdbedrooms 1 8.2561e+10 7.3676e+13 322958
## + housingMedianAge:medianIncome 1 7.1762e+10 7.3687e+13 322960
## + sdrooms:medianIncome 1 6.3522e+10 7.3695e+13 322962
## + latitude:housingMedianAge 1 5.6683e+10 7.3702e+13 322963
## + longitude:housingMedianAge 1 4.4601e+10 7.3714e+13 322965
## + sdbedrooms:medianIncome 1 4.3961e+10 7.3715e+13 322966
## + longitude:population 1 4.2959e+10 7.3716e+13 322966
## + latitude:population 1 3.8959e+10 7.3720e+13 322966
## + housingMedianAge:sdrooms 1 2.0297e+10 7.3738e+13 322970
## <none> 7.3759e+13 322972
## + housingMedianAge:sdbedrooms 1 5.2878e+09 7.3753e+13 322973
## + longitude:latitude 1 3.8330e+09 7.3755e+13 322973
## + housingMedianAge:population 1 8.0282e+08 7.3758e+13 322974
## + sdrooms:population 1 5.1729e+07 7.3759e+13 322974
## - sdbedrooms:population 1 3.3918e+11 7.4098e+13 323036
## - longitude:sdbedrooms 1 7.1904e+11 7.4478e+13 323110
## - longitude:sdrooms 1 9.0747e+11 7.4666e+13 323147
## - latitude:sdbedrooms 1 1.1151e+12 7.4874e+13 323187
## - longitude:medianIncome 1 1.2426e+12 7.5001e+13 323211
## - housingMedianAge 1 1.4460e+12 7.5205e+13 323251
## - latitude:medianIncome 1 1.6777e+12 7.5436e+13 323295
## - latitude:sdrooms 1 1.7008e+12 7.5459e+13 323299
##
## Step: AIC=322936.7
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome
##
## Df Sum of Sq RSS AIC
## + sdrooms:population 1 2.4859e+11 7.3319e+13 322890
## + housingMedianAge:medianIncome 1 1.4850e+11 7.3419e+13 322909
## + sdrooms:sdbedrooms 1 7.7061e+10 7.3490e+13 322924
## + latitude:housingMedianAge 1 6.2949e+10 7.3505e+13 322926
## + sdbedrooms:medianIncome 1 5.3911e+10 7.3514e+13 322928
## + latitude:population 1 4.6838e+10 7.3521e+13 322929
## + sdrooms:medianIncome 1 4.6715e+10 7.3521e+13 322929
## + longitude:housingMedianAge 1 4.3415e+10 7.3524e+13 322930
## + longitude:population 1 3.8397e+10 7.3529e+13 322931
## + housingMedianAge:population 1 2.6311e+10 7.3541e+13 322933
## <none> 7.3568e+13 322937
## + housingMedianAge:sdrooms 1 9.1346e+09 7.3558e+13 322937
## + housingMedianAge:sdbedrooms 1 6.7887e+09 7.3561e+13 322937
## + longitude:latitude 1 4.0405e+09 7.3563e+13 322938
## - population:medianIncome 1 1.9111e+11 7.3759e+13 322972
## - sdbedrooms:population 1 3.5319e+11 7.3921e+13 323004
## - longitude:sdbedrooms 1 7.4848e+11 7.4316e+13 323081
## - longitude:sdrooms 1 9.5105e+11 7.4519e+13 323120
## - latitude:sdbedrooms 1 1.1566e+12 7.4724e+13 323160
## - longitude:medianIncome 1 1.2836e+12 7.4851e+13 323185
## - housingMedianAge 1 1.4993e+12 7.5067e+13 323226
## - latitude:medianIncome 1 1.6949e+12 7.5262e+13 323264
## - latitude:sdrooms 1 1.7742e+12 7.5342e+13 323279
##
## Step: AIC=322889.8
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population
##
## Df Sum of Sq RSS AIC
## + housingMedianAge:medianIncome 1 1.5842e+11 7.3161e+13 322861
## + sdrooms:sdbedrooms 1 9.1700e+10 7.3227e+13 322874
## + latitude:housingMedianAge 1 7.1444e+10 7.3248e+13 322878
## + latitude:population 1 6.2195e+10 7.3257e+13 322879
## + sdrooms:medianIncome 1 6.0660e+10 7.3258e+13 322880
## + sdbedrooms:medianIncome 1 5.0830e+10 7.3268e+13 322882
## + longitude:housingMedianAge 1 4.4367e+10 7.3275e+13 322883
## + longitude:population 1 2.7549e+10 7.3291e+13 322886
## + housingMedianAge:sdrooms 1 1.9114e+10 7.3300e+13 322888
## <none> 7.3319e+13 322890
## + housingMedianAge:sdbedrooms 1 8.4512e+09 7.3310e+13 322890
## + longitude:latitude 1 2.2894e+09 7.3317e+13 322891
## + housingMedianAge:population 1 3.3032e+08 7.3319e+13 322892
## - sdrooms:population 1 2.4859e+11 7.3568e+13 322937
## - population:medianIncome 1 4.3964e+11 7.3759e+13 322974
## - sdbedrooms:population 1 6.0136e+11 7.3920e+13 323006
## - longitude:sdbedrooms 1 6.0708e+11 7.3926e+13 323007
## - longitude:sdrooms 1 7.4116e+11 7.4060e+13 323033
## - latitude:sdbedrooms 1 8.5722e+11 7.4176e+13 323056
## - longitude:medianIncome 1 1.1359e+12 7.4455e+13 323110
## - latitude:sdrooms 1 1.2187e+12 7.4538e+13 323126
## - latitude:medianIncome 1 1.4414e+12 7.4760e+13 323169
## - housingMedianAge 1 1.5083e+12 7.4827e+13 323182
##
## Step: AIC=322860.5
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome
##
## Df Sum of Sq RSS AIC
## + housingMedianAge:sdrooms 1 1.2513e+11 7.3035e+13 322838
## + sdrooms:sdbedrooms 1 8.9314e+10 7.3071e+13 322845
## + sdbedrooms:medianIncome 1 6.4254e+10 7.3096e+13 322850
## + latitude:population 1 6.0719e+10 7.3100e+13 322851
## + latitude:housingMedianAge 1 5.5174e+10 7.3105e+13 322852
## + longitude:housingMedianAge 1 4.5342e+10 7.3115e+13 322854
## + sdrooms:medianIncome 1 3.9590e+10 7.3121e+13 322855
## + longitude:population 1 2.7561e+10 7.3133e+13 322857
## <none> 7.3161e+13 322861
## + housingMedianAge:sdbedrooms 1 4.3703e+09 7.3156e+13 322862
## + housingMedianAge:population 1 2.7004e+09 7.3158e+13 322862
## + longitude:latitude 1 2.5155e+09 7.3158e+13 322862
## - housingMedianAge:medianIncome 1 1.5842e+11 7.3319e+13 322890
## - sdrooms:population 1 2.5851e+11 7.3419e+13 322909
## - population:medianIncome 1 5.2354e+11 7.3684e+13 322962
## - longitude:sdbedrooms 1 5.9948e+11 7.3760e+13 322976
## - sdbedrooms:population 1 6.0127e+11 7.3762e+13 322977
## - longitude:sdrooms 1 7.3213e+11 7.3893e+13 323002
## - latitude:sdbedrooms 1 8.4144e+11 7.4002e+13 323024
## - longitude:medianIncome 1 9.8045e+11 7.4141e+13 323051
## - latitude:sdrooms 1 1.1929e+12 7.4353e+13 323092
## - latitude:medianIncome 1 1.2658e+12 7.4426e+13 323106
##
## Step: AIC=322837.8
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms
##
## Df Sum of Sq RSS AIC
## + housingMedianAge:sdbedrooms 1 2.0330e+11 7.2832e+13 322799
## + sdrooms:medianIncome 1 1.1912e+11 7.2916e+13 322816
## + latitude:population 1 6.4505e+10 7.2971e+13 322827
## + longitude:housingMedianAge 1 5.0558e+10 7.2985e+13 322830
## + latitude:housingMedianAge 1 3.7219e+10 7.2998e+13 322832
## + longitude:population 1 2.7187e+10 7.3008e+13 322834
## + sdbedrooms:medianIncome 1 1.7732e+10 7.3018e+13 322836
## + sdrooms:sdbedrooms 1 1.1940e+10 7.3023e+13 322837
## <none> 7.3035e+13 322838
## + longitude:latitude 1 1.8768e+09 7.3034e+13 322839
## + housingMedianAge:population 1 4.1898e+08 7.3035e+13 322840
## - housingMedianAge:sdrooms 1 1.2513e+11 7.3161e+13 322861
## - housingMedianAge:medianIncome 1 2.6444e+11 7.3300e+13 322888
## - sdrooms:population 1 2.9521e+11 7.3331e+13 322894
## - population:medianIncome 1 5.6254e+11 7.3598e+13 322947
## - sdbedrooms:population 1 5.6951e+11 7.3605e+13 322948
## - longitude:sdbedrooms 1 6.0376e+11 7.3639e+13 322955
## - longitude:sdrooms 1 6.9501e+11 7.3730e+13 322973
## - latitude:sdbedrooms 1 8.5327e+11 7.3889e+13 323004
## - longitude:medianIncome 1 1.0333e+12 7.4069e+13 323039
## - latitude:sdrooms 1 1.1809e+12 7.4216e+13 323067
## - latitude:medianIncome 1 1.3407e+12 7.4376e+13 323099
##
## Step: AIC=322799.5
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms + housingMedianAge:sdbedrooms
##
## Df Sum of Sq RSS AIC
## + sdrooms:medianIncome 1 1.2419e+11 7.2708e+13 322777
## + longitude:housingMedianAge 1 5.8030e+10 7.2774e+13 322790
## + latitude:population 1 5.5480e+10 7.2777e+13 322790
## + sdrooms:sdbedrooms 1 5.0337e+10 7.2782e+13 322792
## + sdbedrooms:medianIncome 1 4.7501e+10 7.2785e+13 322792
## + longitude:population 1 2.3455e+10 7.2809e+13 322797
## + latitude:housingMedianAge 1 2.3381e+10 7.2809e+13 322797
## <none> 7.2832e+13 322799
## + longitude:latitude 1 1.9414e+09 7.2830e+13 322801
## + housingMedianAge:population 1 1.6714e+06 7.2832e+13 322801
## - housingMedianAge:sdbedrooms 1 2.0330e+11 7.3035e+13 322838
## - housingMedianAge:sdrooms 1 3.2406e+11 7.3156e+13 322862
## - longitude:sdbedrooms 1 3.4441e+11 7.3177e+13 322866
## - sdrooms:population 1 3.6124e+11 7.3193e+13 322869
## - longitude:sdrooms 1 4.2024e+11 7.3252e+13 322881
## - housingMedianAge:medianIncome 1 4.6756e+11 7.3300e+13 322890
## - latitude:sdbedrooms 1 5.3710e+11 7.3369e+13 322904
## - population:medianIncome 1 6.2668e+11 7.3459e+13 322921
## - sdbedrooms:population 1 6.4206e+11 7.3474e+13 322924
## - latitude:sdrooms 1 7.5537e+11 7.3587e+13 322947
## - longitude:medianIncome 1 8.7762e+11 7.3710e+13 322971
## - latitude:medianIncome 1 1.1764e+12 7.4009e+13 323029
##
## Step: AIC=322776.8
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms + housingMedianAge:sdbedrooms +
## sdrooms:medianIncome
##
## Df Sum of Sq RSS AIC
## + sdbedrooms:medianIncome 1 2.9592e+11 7.2412e+13 322720
## + sdrooms:sdbedrooms 1 7.4758e+10 7.2633e+13 322764
## + longitude:housingMedianAge 1 5.9983e+10 7.2648e+13 322767
## + latitude:population 1 5.1482e+10 7.2656e+13 322769
## + longitude:population 1 2.1932e+10 7.2686e+13 322774
## + latitude:housingMedianAge 1 1.9584e+10 7.2688e+13 322775
## <none> 7.2708e+13 322777
## + longitude:latitude 1 2.0298e+09 7.2706e+13 322778
## + housingMedianAge:population 1 7.4412e+06 7.2708e+13 322779
## - sdrooms:medianIncome 1 1.2419e+11 7.2832e+13 322799
## - housingMedianAge:sdbedrooms 1 2.0838e+11 7.2916e+13 322816
## - longitude:sdbedrooms 1 3.6276e+11 7.3071e+13 322847
## - longitude:sdrooms 1 3.8753e+11 7.3095e+13 322852
## - housingMedianAge:sdrooms 1 3.9620e+11 7.3104e+13 322853
## - sdrooms:population 1 4.0154e+11 7.3109e+13 322854
## - housingMedianAge:medianIncome 1 4.9001e+11 7.3198e+13 322872
## - latitude:sdbedrooms 1 5.6513e+11 7.3273e+13 322887
## - population:medianIncome 1 6.2590e+11 7.3334e+13 322899
## - sdbedrooms:population 1 6.8961e+11 7.3398e+13 322911
## - latitude:sdrooms 1 7.2419e+11 7.3432e+13 322918
## - longitude:medianIncome 1 8.7596e+11 7.3584e+13 322948
## - latitude:medianIncome 1 1.1775e+12 7.3885e+13 323007
##
## Step: AIC=322719.9
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms + housingMedianAge:sdbedrooms +
## sdrooms:medianIncome + sdbedrooms:medianIncome
##
## Df Sum of Sq RSS AIC
## + longitude:housingMedianAge 1 5.8945e+10 7.2353e+13 322710
## + latitude:population 1 4.6856e+10 7.2365e+13 322713
## + sdrooms:sdbedrooms 1 4.0375e+10 7.2372e+13 322714
## + latitude:housingMedianAge 1 2.0574e+10 7.2391e+13 322718
## + longitude:population 1 1.6530e+10 7.2395e+13 322719
## <none> 7.2412e+13 322720
## + longitude:latitude 1 6.1868e+08 7.2411e+13 322722
## + housingMedianAge:population 1 5.9584e+06 7.2412e+13 322722
## - longitude:sdbedrooms 1 2.5010e+11 7.2662e+13 322768
## - sdbedrooms:medianIncome 1 2.9592e+11 7.2708e+13 322777
## - longitude:sdrooms 1 3.0618e+11 7.2718e+13 322779
## - housingMedianAge:sdbedrooms 1 3.2712e+11 7.2739e+13 322783
## - sdrooms:medianIncome 1 3.7261e+11 7.2785e+13 322792
## - sdrooms:population 1 4.2932e+11 7.2841e+13 322803
## - latitude:sdbedrooms 1 4.3262e+11 7.2845e+13 322804
## - housingMedianAge:sdrooms 1 4.5764e+11 7.2870e+13 322809
## - housingMedianAge:medianIncome 1 5.4787e+11 7.2960e+13 322827
## - latitude:sdrooms 1 6.1234e+11 7.3024e+13 322840
## - population:medianIncome 1 6.5043e+11 7.3062e+13 322847
## - sdbedrooms:population 1 6.8377e+11 7.3096e+13 322854
## - longitude:medianIncome 1 1.0252e+12 7.3437e+13 322921
## - latitude:medianIncome 1 1.3590e+12 7.3771e+13 322987
##
## Step: AIC=322710.2
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms + housingMedianAge:sdbedrooms +
## sdrooms:medianIncome + sdbedrooms:medianIncome + longitude:housingMedianAge
##
## Df Sum of Sq RSS AIC
## + latitude:housingMedianAge 1 1.3755e+12 7.0978e+13 322435
## + latitude:population 1 8.6357e+10 7.2267e+13 322695
## + longitude:population 1 4.3927e+10 7.2309e+13 322703
## + sdrooms:sdbedrooms 1 4.1558e+10 7.2311e+13 322704
## <none> 7.2353e+13 322710
## + longitude:latitude 1 3.8125e+09 7.2349e+13 322711
## + housingMedianAge:population 1 6.7888e+08 7.2352e+13 322712
## - longitude:housingMedianAge 1 5.8945e+10 7.2412e+13 322720
## - longitude:sdbedrooms 1 2.4264e+11 7.2596e+13 322757
## - longitude:sdrooms 1 2.8810e+11 7.2641e+13 322766
## - sdbedrooms:medianIncome 1 2.9488e+11 7.2648e+13 322767
## - housingMedianAge:sdbedrooms 1 3.3612e+11 7.2689e+13 322775
## - sdrooms:medianIncome 1 3.7457e+11 7.2728e+13 322783
## - latitude:sdbedrooms 1 4.3290e+11 7.2786e+13 322794
## - sdrooms:population 1 4.3370e+11 7.2787e+13 322794
## - housingMedianAge:sdrooms 1 4.7253e+11 7.2826e+13 322802
## - housingMedianAge:medianIncome 1 5.6086e+11 7.2914e+13 322820
## - latitude:sdrooms 1 6.1113e+11 7.2964e+13 322830
## - population:medianIncome 1 6.5291e+11 7.3006e+13 322838
## - sdbedrooms:population 1 6.5827e+11 7.3011e+13 322839
## - longitude:medianIncome 1 1.0187e+12 7.3372e+13 322910
## - latitude:medianIncome 1 1.3534e+12 7.3706e+13 322976
##
## Step: AIC=322434.9
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms + housingMedianAge:sdbedrooms +
## sdrooms:medianIncome + sdbedrooms:medianIncome + longitude:housingMedianAge +
## latitude:housingMedianAge
##
## Df Sum of Sq RSS AIC
## + sdrooms:sdbedrooms 1 6.7530e+10 7.0910e+13 322423
## + latitude:population 1 3.5088e+10 7.0942e+13 322430
## + longitude:population 1 3.1194e+10 7.0946e+13 322431
## <none> 7.0978e+13 322435
## + longitude:latitude 1 3.7302e+09 7.0974e+13 322436
## + housingMedianAge:population 1 1.8430e+08 7.0977e+13 322437
## - housingMedianAge:medianIncome 1 7.5821e+10 7.1053e+13 322448
## - housingMedianAge:sdrooms 1 9.3531e+10 7.1071e+13 322452
## - housingMedianAge:sdbedrooms 1 1.3754e+11 7.1115e+13 322461
## - longitude:sdbedrooms 1 2.7961e+11 7.1257e+13 322490
## - sdrooms:medianIncome 1 2.9170e+11 7.1269e+13 322492
## - sdbedrooms:medianIncome 1 3.0578e+11 7.1283e+13 322495
## - longitude:sdrooms 1 3.1188e+11 7.1289e+13 322496
## - latitude:sdbedrooms 1 4.9886e+11 7.1476e+13 322534
## - sdrooms:population 1 5.0556e+11 7.1483e+13 322535
## - sdbedrooms:population 1 6.3506e+11 7.1613e+13 322562
## - latitude:sdrooms 1 6.5516e+11 7.1633e+13 322566
## - population:medianIncome 1 7.4583e+11 7.1723e+13 322584
## - latitude:housingMedianAge 1 1.3755e+12 7.2353e+13 322710
## - longitude:housingMedianAge 1 1.4139e+12 7.2391e+13 322718
## - longitude:medianIncome 1 1.4521e+12 7.2430e+13 322725
## - latitude:medianIncome 1 1.8996e+12 7.2877e+13 322814
##
## Step: AIC=322423.1
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms + housingMedianAge:sdbedrooms +
## sdrooms:medianIncome + sdbedrooms:medianIncome + longitude:housingMedianAge +
## latitude:housingMedianAge + sdrooms:sdbedrooms
##
## Df Sum of Sq RSS AIC
## + latitude:population 1 3.9988e+10 7.0870e+13 322417
## + longitude:population 1 3.0350e+10 7.0880e+13 322419
## <none> 7.0910e+13 322423
## + longitude:latitude 1 2.9439e+09 7.0907e+13 322425
## + housingMedianAge:population 1 1.3674e+07 7.0910e+13 322425
## - housingMedianAge:medianIncome 1 5.7916e+10 7.0968e+13 322433
## - housingMedianAge:sdrooms 1 6.5219e+10 7.0975e+13 322434
## - sdrooms:sdbedrooms 1 6.7530e+10 7.0978e+13 322435
## - housingMedianAge:sdbedrooms 1 1.7250e+11 7.1083e+13 322456
## - sdbedrooms:medianIncome 1 2.6247e+11 7.1172e+13 322474
## - sdrooms:medianIncome 1 2.9734e+11 7.1207e+13 322482
## - longitude:sdbedrooms 1 3.0057e+11 7.1211e+13 322482
## - longitude:sdrooms 1 3.7035e+11 7.1280e+13 322496
## - sdrooms:population 1 5.1515e+11 7.1425e+13 322526
## - latitude:sdbedrooms 1 5.3298e+11 7.1443e+13 322529
## - sdbedrooms:population 1 5.5143e+11 7.1461e+13 322533
## - latitude:sdrooms 1 7.2224e+11 7.1632e+13 322568
## - population:medianIncome 1 7.4014e+11 7.1650e+13 322571
## - latitude:housingMedianAge 1 1.4015e+12 7.2311e+13 322704
## - longitude:housingMedianAge 1 1.4408e+12 7.2351e+13 322712
## - longitude:medianIncome 1 1.5058e+12 7.2416e+13 322725
## - latitude:medianIncome 1 1.9603e+12 7.2870e+13 322815
##
## Step: AIC=322417
## medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms + housingMedianAge:sdbedrooms +
## sdrooms:medianIncome + sdbedrooms:medianIncome + longitude:housingMedianAge +
## latitude:housingMedianAge + sdrooms:sdbedrooms + latitude:population
##
## Df Sum of Sq RSS AIC
## <none> 7.0870e+13 322417
## + longitude:latitude 1 2.3323e+09 7.0868e+13 322418
## + longitude:population 1 1.6253e+09 7.0868e+13 322419
## + housingMedianAge:population 1 6.4015e+08 7.0869e+13 322419
## - latitude:population 1 3.9988e+10 7.0910e+13 322423
## - housingMedianAge:medianIncome 1 5.8955e+10 7.0929e+13 322427
## - housingMedianAge:sdrooms 1 6.5397e+10 7.0935e+13 322428
## - sdrooms:sdbedrooms 1 7.2430e+10 7.0942e+13 322430
## - housingMedianAge:sdbedrooms 1 1.7061e+11 7.1041e+13 322450
## - sdbedrooms:medianIncome 1 2.5649e+11 7.1126e+13 322467
## - sdrooms:medianIncome 1 2.9190e+11 7.1162e+13 322474
## - longitude:sdbedrooms 1 2.9926e+11 7.1169e+13 322476
## - longitude:sdrooms 1 3.6562e+11 7.1236e+13 322489
## - latitude:sdbedrooms 1 5.2818e+11 7.1398e+13 322522
## - sdrooms:population 1 5.3072e+11 7.1401e+13 322523
## - sdbedrooms:population 1 5.6379e+11 7.1434e+13 322529
## - latitude:sdrooms 1 7.2264e+11 7.1593e+13 322562
## - population:medianIncome 1 7.6104e+11 7.1631e+13 322569
## - latitude:housingMedianAge 1 1.3485e+12 7.2219e+13 322687
## - longitude:housingMedianAge 1 1.4436e+12 7.2314e+13 322706
## - longitude:medianIncome 1 1.5033e+12 7.2373e+13 322718
## - latitude:medianIncome 1 1.9613e+12 7.2831e+13 322809##
## Call:
## lm(formula = medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome + sdbedrooms:population +
## latitude:sdrooms + latitude:medianIncome + latitude:sdbedrooms +
## longitude:medianIncome + longitude:sdrooms + longitude:sdbedrooms +
## population:medianIncome + sdrooms:population + housingMedianAge:medianIncome +
## housingMedianAge:sdrooms + housingMedianAge:sdbedrooms +
## sdrooms:medianIncome + sdbedrooms:medianIncome + longitude:housingMedianAge +
## latitude:housingMedianAge + sdrooms:sdbedrooms + latitude:population,
## data = cahousing_train)
##
## Coefficients:
## (Intercept) longitude
## 1.730e+06 2.118e+04
## latitude housingMedianAge
## 2.406e+04 -1.058e+05
## sdrooms sdbedrooms
## 4.825e+05 -2.252e+06
## population medianIncome
## -6.961e+01 -8.808e+05
## sdbedrooms:population latitude:sdrooms
## 5.059e+01 7.770e+03
## latitude:medianIncome latitude:sdbedrooms
## -1.309e+04 -3.554e+04
## longitude:medianIncome longitude:sdrooms
## -1.153e+04 6.310e+03
## longitude:sdbedrooms population:medianIncome
## -2.916e+04 5.767e+00
## sdrooms:population housingMedianAge:medianIncome
## -6.664e+00 1.329e+02
## housingMedianAge:sdrooms housingMedianAge:sdbedrooms
## -2.137e+02 1.904e+03
## sdrooms:medianIncome sdbedrooms:medianIncome
## -1.462e+03 1.021e+04
## longitude:housingMedianAge latitude:housingMedianAge
## -1.238e+03 -1.201e+03
## sdrooms:sdbedrooms latitude:population
## -1.838e+02 7.962e-01## n= 14447
##
## node), split, n, deviance, yval
## * denotes terminal node
##
## 1) root 14447 1.939459e+14 207357.60
## 2) medianIncome< 5.1322 11572 9.974003e+13 175391.00
## 4) medianIncome< 3.1288 5730 3.356451e+13 137938.30
## 8) sdrooms>=4.211321 3617 1.561711e+13 120906.20
## 16) medianIncome< 2.5115 1949 5.999051e+12 100440.90
## 32) latitude>=34.725 1317 2.969069e+12 91332.35
## 64) longitude>=-119.905 343 1.405326e+11 65610.79
## 128) sdrooms< 5.336627 251 7.131474e+10 61331.47
## 256) housingMedianAge>=10.5 243 4.244858e+10 60320.99
## 512) medianIncome< 1.8322 108 7.340834e+09 54592.59 *
## 513) medianIncome>=1.8322 135 2.872861e+10 64903.70
## 1026) latitude< 36.795 121 2.038704e+10 62953.72 *
## 1027) latitude>=36.795 14 3.904934e+09 81757.14 *
## 257) housingMedianAge< 10.5 8 2.108130e+10 92025.00 *
## 129) sdrooms>=5.336627 92 5.208113e+10 77285.87
## 258) housingMedianAge>=24.5 45 1.912503e+10 67846.67
## 516) population>=563.5 38 1.225582e+10 64313.16
## 1032) medianIncome< 2.24735 26 4.392465e+09 58246.15 *
## 1033) medianIncome>=2.24735 12 4.832789e+09 77458.33 *
## 517) population< 563.5 7 3.819134e+09 87028.57 *
## 259) housingMedianAge< 24.5 47 2.510784e+10 86323.40
## 518) population>=1179.5 18 4.091765e+09 75183.33 *
## 519) population< 1179.5 29 1.739575e+10 93237.93
## 1038) latitude< 36.045 11 8.598967e+09 82245.45 *
## 1039) latitude>=36.045 18 6.655324e+09 99955.56 *
## 65) longitude< -119.905 974 2.521694e+12 100390.30
## 130) latitude>=38.955 375 2.687034e+11 80839.46
## 260) housingMedianAge>=20.5 226 1.140167e+11 74241.59
## 520) housingMedianAge< 48.5 205 7.762388e+10 72264.39
## 1040) longitude>=-122.695 144 4.483980e+10 69123.61
## 2080) sdrooms< 7.8741 136 2.482652e+10 67515.44
## 4160) medianIncome< 1.8071 42 5.233759e+09 60895.24 *
## 4161) medianIncome>=1.8071 94 1.692956e+10 70473.40 *
## 2081) sdrooms>=7.8741 8 1.368224e+10 96462.50 *
## 1041) longitude< -122.695 61 2.801033e+10 79678.67
## 2082) latitude>=39.585 47 1.551515e+10 73759.55
## 4164) medianIncome< 1.93295 16 3.805300e+09 59874.94 *
## 4165) medianIncome>=1.93295 31 7.033319e+09 80925.81 *
## 2083) latitude< 39.585 14 5.320315e+09 99550.00 *
## 521) housingMedianAge>=48.5 21 2.776809e+10 93542.86
## 1042) latitude>=39.95 11 4.451327e+09 75045.45 *
## 1043) latitude< 39.95 10 1.541301e+10 113890.00 *
## 261) housingMedianAge< 20.5 149 1.299261e+11 90846.97
## 522) latitude>=39.365 108 6.091001e+10 84783.32
## 1044) longitude< -121.965 60 2.734058e+10 78566.65
## 2088) sdbedrooms>=1.601064 8 3.834866e+09 58862.38 *
## 2089) sdbedrooms< 1.601064 52 1.992179e+10 81598.08
## 4178) medianIncome>=1.9186 41 1.186846e+10 78548.78
## 8356) medianIncome< 2.22745 21 2.665870e+09 70995.24 *
## 8357) medianIncome>=2.22745 20 6.746332e+09 86480.00 *
## 4179) medianIncome< 1.9186 11 6.251165e+09 92963.64 *
## 1045) longitude>=-121.965 48 2.835208e+10 92554.17
## 2090) housingMedianAge>=13.5 41 1.463044e+10 87300.00
## 4180) latitude>=39.88 8 2.312960e+09 73750.00 *
## 4181) latitude< 39.88 33 1.049258e+10 90584.85
## 8362) medianIncome< 1.66285 7 1.570900e+09 74800.00 *
## 8363) medianIncome>=1.66285 26 6.707979e+09 94834.62 *
## 2091) housingMedianAge< 13.5 7 5.960334e+09 123328.60 *
## 523) latitude< 39.365 41 5.458514e+10 106819.50
## 1046) longitude< -121.345 30 2.996395e+10 94613.33
## 2092) longitude>=-122.655 13 3.138068e+09 72930.77 *
## 2093) longitude< -122.655 17 1.604047e+10 111194.10 *
## 1047) longitude>=-121.345 11 7.961309e+09 140109.10 *
## 131) latitude< 38.955 599 2.019915e+12 112630.10
## 262) longitude>=-121.555 372 8.222264e+11 97058.07
## 524) population>=100.5 361 4.988023e+11 94281.44
## 1048) latitude>=35.705 343 3.535885e+11 90713.99
## 2096) medianIncome< 1.87195 106 6.171196e+10 75405.66
## 4192) latitude< 37.19 19 2.688221e+09 59268.42 *
## 4193) latitude>=37.19 87 5.299538e+10 78929.89
## 8386) longitude< -121.225 52 3.199957e+10 70459.62
## 16772) medianIncome< 1.66625 25 1.828700e+09 61360.00 *
## 16773) medianIncome>=1.66625 27 2.618405e+10 78885.19
## 33546) medianIncome>=1.7537 20 1.265412e+10 71110.00
## 67092) housingMedianAge< 42.5 13 1.253169e+09 62807.69 *
## 67093) housingMedianAge>=42.5 7 8.840754e+09 86528.57 *
## 33547) medianIncome< 1.7537 7 8.866380e+09 101100.00 *
## 8387) longitude>=-121.225 35 1.172220e+10 91514.29
## 16774) longitude>=-121.01 27 4.661027e+09 87111.11 *
## 16775) longitude< -121.01 8 4.770975e+09 106375.00 *
## 2097) medianIncome>=1.87195 237 2.559258e+11 97560.76
## 4194) housingMedianAge>=33.5 86 4.734643e+10 83746.51
## 8388) sdrooms< 5.504795 74 3.249330e+10 80120.27
## 16776) medianIncome< 2.0573 22 7.505173e+09 70040.91 *
## 16777) medianIncome>=2.0573 52 2.180747e+10 84384.62
## 33554) latitude< 37.985 34 8.739099e+09 79194.12
## 67108) latitude>=37.9 8 4.673950e+08 66175.00 *
## 67109) latitude< 37.9 26 6.498500e+09 83200.00
## 134218) latitude< 37.63 16 1.888630e+09 74825.00 *
## 134219) latitude>=37.63 10 1.692020e+09 96600.00 *
## 33555) latitude>=37.985 18 1.042214e+10 94188.89 *
## 8389) sdrooms>=5.504795 12 7.879449e+09 106108.30 *
## 4195) housingMedianAge< 33.5 151 1.828207e+11 105428.50
## 8390) population>=279 142 1.445576e+11 102764.80
## 16780) housingMedianAge>=15.5 116 9.904730e+10 98686.21
## 33560) population>=741 86 6.239299e+10 94872.09
## 67120) latitude< 38.595 61 4.203022e+10 89226.23
## 134240) sdrooms< 5.572404 46 3.037689e+10 85119.57
## 268480) latitude< 37.03 9 4.211560e+09 71600.00 *
## 268481) latitude>=37.03 37 2.412019e+10 88408.11
## 536962) longitude< -121.015 22 8.410918e+09 79890.91 *
## 536963) longitude>=-121.015 15 1.177262e+10 100900.00 *
## 134241) sdrooms>=5.572404 15 8.498504e+09 101820.00 *
## 67121) latitude>=38.595 25 1.367396e+10 108648.00
## 134242) medianIncome< 2.10995 7 1.938834e+09 86671.43 *
## 134243) medianIncome>=2.10995 18 7.039589e+09 117194.40 *
## 33561) population< 741 30 3.181679e+10 109620.00
## 67122) longitude>=-120.875 18 8.563060e+09 99233.33 *
## 67123) longitude< -120.875 12 1.839900e+10 125200.00 *
## 16781) housingMedianAge< 15.5 26 3.497150e+10 120961.50
## 33562) latitude< 37.55 8 9.168749e+09 92012.50 *
## 33563) latitude>=37.55 18 1.611866e+10 133827.80 *
## 8391) population< 279 9 2.135906e+10 147455.60 *
## 1049) latitude< 35.705 18 5.766634e+10 162261.10 *
## 525) population< 100.5 11 2.293018e+11 188181.90 *
## 263) longitude< -121.555 227 9.596586e+11 138148.90
## 526) latitude>=37.725 194 5.678340e+11 125512.90
## 1052) sdbedrooms>=0.9688375 184 3.942679e+11 121433.20
## 2104) longitude>=-122.375 147 1.487738e+11 112926.50
## 4208) latitude< 38.175 123 7.565047e+10 106652.00
## 8416) housingMedianAge< 47.5 76 2.758460e+10 99507.89
## 16832) latitude< 37.775 27 6.196656e+09 90929.63 *
## 16833) latitude>=37.775 49 1.830631e+10 104234.70
## 33666) latitude>=37.925 29 7.400808e+09 96037.93
## 67332) medianIncome< 1.9428 11 1.099436e+09 85018.18 *
## 67333) medianIncome>=1.9428 18 4.149276e+09 102772.20 *
## 33667) latitude< 37.925 20 6.131872e+09 116120.00 *
## 8417) housingMedianAge>=47.5 47 3.791460e+10 118204.30
## 16834) medianIncome< 1.5437 9 1.349642e+09 86944.44 *
## 16835) medianIncome>=1.5437 38 2.568745e+10 125607.90
## 33670) sdrooms>=4.578056 24 1.355353e+10 116733.30
## 67340) sdbedrooms< 1.084085 12 3.824337e+09 105583.30 *
## 67341) sdbedrooms>=1.084085 12 6.745457e+09 127883.30 *
## 33671) sdrooms< 4.578056 14 7.003404e+09 140821.40 *
## 4209) latitude>=38.175 24 4.346343e+10 145083.30
## 8418) housingMedianAge>=23.5 16 1.908722e+10 126187.50 *
## 8419) housingMedianAge< 23.5 8 7.237695e+09 182875.00 *
## 2105) longitude< -122.375 37 1.925951e+11 155229.70
## 4210) latitude>=38.66 9 1.773040e+09 85433.33 *
## 4211) latitude< 38.66 28 1.328856e+11 177664.30
## 8422) latitude>=38.015 21 3.967017e+10 157933.30
## 16844) population< 752.5 7 7.412174e+09 116128.60 *
## 16845) population>=752.5 14 1.390779e+10 178835.70 *
## 8423) latitude< 38.015 7 6.051332e+10 236857.10 *
## 1053) sdbedrooms< 0.9688375 10 1.141529e+11 200580.00 *
## 527) latitude< 37.725 33 1.787490e+11 212433.30
## 1054) sdbedrooms< 1.175337 25 8.522519e+10 189032.00
## 2108) medianIncome>=2.1999 13 2.621792e+10 165676.90 *
## 2109) medianIncome< 2.1999 12 4.423441e+10 214333.30 *
## 1055) sdbedrooms>=1.175337 8 3.705024e+10 285562.50 *
## 33) latitude< 34.725 632 2.693018e+12 119422.00
## 66) longitude>=-118.315 572 1.897569e+12 111659.60
## 132) longitude>=-117.355 307 6.551340e+11 95475.90
## 264) longitude>=-116.45 69 2.099679e+10 65331.88
## 528) medianIncome< 1.549 19 2.026180e+09 53800.00 *
## 529) medianIncome>=1.549 50 1.548376e+10 69714.00
## 1058) housingMedianAge>=19.5 20 2.102002e+09 59570.00 *
## 1059) housingMedianAge< 19.5 30 9.951734e+09 76476.67 *
## 265) longitude< -116.45 238 5.532625e+11 104215.10
## 530) latitude>=33.695 153 9.559306e+10 87475.82
## 1060) housingMedianAge>=27.5 66 1.140906e+10 76751.52 *
## 1061) housingMedianAge< 27.5 87 7.083483e+10 95611.49
## 2122) sdrooms< 6.746613 76 3.780486e+10 91709.21
## 4244) longitude>=-116.78 10 9.364360e+08 67880.00 *
## 4245) longitude< -116.78 66 3.032976e+10 95319.70
## 8490) medianIncome< 2.14745 45 1.781415e+10 89928.89
## 16980) population>=1174.5 29 2.303961e+09 84082.76 *
## 16981) population< 1174.5 16 1.272261e+10 100525.00 *
## 8491) medianIncome>=2.14745 21 8.405583e+09 106871.40 *
## 2123) sdrooms>=6.746613 11 2.387666e+10 122572.70 *
## 531) latitude< 33.695 85 3.376299e+11 134345.90
## 1062) latitude< 32.715 31 1.483823e+10 101161.30
## 2124) medianIncome< 2.09045 20 2.494306e+09 89135.00 *
## 2125) medianIncome>=2.09045 11 4.191962e+09 123027.30 *
## 1063) latitude>=32.715 54 2.690563e+11 153396.30
## 2126) population>=1098.5 30 3.167792e+10 127683.30
## 4252) sdrooms< 5.114728 22 1.097006e+10 117090.90
## 8504) sdrooms>=4.44788 12 5.568442e+09 107975.00 *
## 8505) sdrooms< 4.44788 10 3.207781e+09 128030.00 *
## 4253) sdrooms>=5.114728 8 1.145141e+10 156812.50 *
## 2127) population< 1098.5 24 1.927504e+11 185537.50
## 4254) latitude>=33.125 10 1.018004e+10 127940.00 *
## 4255) latitude< 33.125 14 1.256994e+11 226678.60 *
## 133) longitude< -117.355 265 1.068877e+12 130408.30
## 266) latitude>=33.865 230 3.739382e+11 119893.90
## 532) population>=254.5 223 1.930605e+11 116170.90
## 1064) medianIncome< 2.16855 147 7.485186e+10 107295.90
## 2128) latitude< 34.005 106 2.076199e+10 101706.60 *
## 2129) latitude>=34.005 41 4.221698e+10 121746.30
## 4258) longitude>=-117.645 8 3.588195e+09 87275.00 *
## 4259) longitude< -117.645 33 2.681807e+10 130103.00
## 8518) population< 918.5 9 1.371709e+09 108188.90 *
## 8519) population>=918.5 24 1.950352e+10 138320.80
## 17038) sdrooms>=4.566226 11 4.376280e+09 124600.00 *
## 17039) sdrooms< 4.566226 13 1.130409e+10 149930.80 *
## 1065) medianIncome>=2.16855 76 8.423522e+10 133336.80
## 2130) longitude>=-117.81 22 8.876450e+09 113404.50 *
## 2131) longitude< -117.81 54 6.305729e+10 141457.40
## 4262) longitude< -118.165 25 3.431156e+10 125860.00
## 8524) longitude>=-118.275 18 7.851460e+09 116033.30 *
## 8525) longitude< -118.275 7 2.025245e+10 151128.60 *
## 4263) longitude>=-118.165 29 1.742067e+10 154903.40
## 8526) latitude>=34.11 13 5.714428e+09 141769.20 *
## 8527) latitude< 34.11 16 7.641530e+09 165575.00 *
## 533) population< 254.5 7 7.931488e+10 238500.00 *
## 267) latitude< 33.865 35 5.024190e+11 199502.90
## 534) housingMedianAge>=24.5 19 9.838664e+10 153336.80 *
## 535) housingMedianAge< 24.5 16 3.154498e+11 254325.20 *
## 67) longitude< -118.315 60 4.324115e+11 193423.30
## 134) sdbedrooms< 1.374138 53 2.226323e+11 176832.10
## 268) latitude< 34.045 31 5.225143e+10 151338.70
## 536) housingMedianAge>=42.5 21 1.949220e+10 138328.60
## 1072) latitude< 34.005 8 6.957388e+08 121137.50 *
## 1073) latitude>=34.005 13 1.497727e+10 148907.70 *
## 537) housingMedianAge< 42.5 10 2.174016e+10 178660.00 *
## 269) latitude>=34.045 22 1.218443e+11 212754.50
## 538) population>=1026 8 2.360995e+10 167387.50 *
## 539) population< 1026 14 7.236024e+10 238678.60 *
## 135) sdbedrooms>=1.374138 7 8.472798e+10 319042.90 *
## 17) medianIncome>=2.5115 1668 7.847958e+12 144819.10
## 34) sdrooms>=4.931884 944 3.323308e+12 127620.60
## 68) housingMedianAge< 48.5 887 2.616763e+12 123748.30
## 136) latitude>=34.675 630 1.460739e+12 115112.90
## 272) longitude>=-120.225 185 1.462574e+11 87090.27
## 544) sdbedrooms< 1.306651 156 7.214896e+10 80714.74
## 1088) housingMedianAge>=20.5 106 3.813023e+10 76793.40
## 2176) sdrooms< 5.952425 81 1.692036e+10 73544.44
## 4352) longitude< -119.345 48 5.729415e+09 69227.08 *
## 4353) longitude>=-119.345 33 8.994861e+09 79824.24
## 8706) medianIncome>=2.60705 26 5.472730e+09 75403.85 *
## 8707) medianIncome< 2.60705 7 1.127097e+09 96242.86 *
## 2177) sdrooms>=5.952425 25 1.758462e+10 87320.00
## 4354) sdbedrooms>=1.09811 15 1.108709e+10 77533.33 *
## 4355) sdbedrooms< 1.09811 10 2.905820e+09 102000.00 *
## 1089) housingMedianAge< 20.5 50 2.893326e+10 89028.00
## 2178) latitude< 36.88 40 2.367792e+10 85020.00
## 4356) latitude>=35.425 27 1.556261e+10 79988.89
## 8712) population>=1529.5 8 2.921660e+09 64850.00 *
## 8713) population< 1529.5 19 1.003546e+10 86363.16 *
## 4357) latitude< 35.425 13 6.012468e+09 95469.23 *
## 2179) latitude>=36.88 10 2.042524e+09 105060.00 *
## 545) sdbedrooms>=1.306651 29 3.365735e+10 121386.20
## 1090) latitude< 38.945 22 2.158266e+10 113677.30
## 2180) population< 1128.5 15 1.068781e+10 104633.30 *
## 2181) population>=1128.5 7 7.038897e+09 133057.10 *
## 1091) latitude>=38.945 7 6.658289e+09 145614.30 *
## 273) longitude< -120.225 445 1.108813e+12 126762.70
## 546) latitude>=37.03 400 6.543659e+11 119855.80
## 1092) latitude>=39.48 82 3.413314e+10 92848.78
## 2184) population< 2077.5 74 2.613176e+10 89868.92
## 4368) longitude>=-123.48 57 1.526715e+10 87035.09 *
## 4369) longitude< -123.48 17 8.872075e+09 99370.59 *
## 2185) population>=2077.5 8 1.266229e+09 120412.50 *
## 1093) latitude< 39.48 318 5.450014e+11 126819.80
## 2186) longitude>=-122.06 245 2.835243e+11 117612.20
## 4372) population>=321.5 229 1.999017e+11 114105.20
## 8744) housingMedianAge>=28.5 89 8.422320e+10 104552.80
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## 43620) sdrooms< 5.529965 7 5.582940e+09 185900.00 *
## 43621) sdrooms>=5.529965 22 3.382481e+10 230795.50
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## 21824) sdrooms< 5.153681 381 3.870956e+11 178755.10
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## 349188) population>=1488 36 1.562632e+10 159936.10
## 698376) sdrooms< 4.51974 15 2.684276e+09 147560.00 *
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## 698378) medianIncome>=3.53365 14 4.570689e+09 167771.40 *
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## 349191) latitude>=34.095 9 7.651536e+09 233577.80 *
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## 87298) sdrooms< 4.503367 99 1.059952e+11 175571.70
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## 349193) sdrooms>=3.892551 29 2.905087e+10 171448.30
## 698386) medianIncome>=3.5843 18 7.052089e+09 162005.60 *
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## 811) latitude< 37.965 129 4.017307e+11 307021.70
## 1622) longitude>=-122.025 116 3.485182e+11 301572.40
## 3244) latitude>=33.525 103 2.480366e+11 296358.30
## 6488) sdrooms>=6.1948 85 1.336731e+11 290642.40
## 12976) sdbedrooms>=1.041178 9 1.853898e+10 257333.30 *
## 12977) sdbedrooms< 1.041178 76 1.039662e+11 294586.80
## 25954) housingMedianAge>=13.5 61 8.482695e+10 289470.50
## 51908) population< 2475 49 5.077318e+10 284104.10
## 103816) sdrooms< 7.394687 39 4.227970e+10 279189.70
## 207632) latitude>=33.74 31 3.224820e+10 273554.80
## 415264) sdrooms>=7.173319 7 1.701931e+10 254885.70 *
## 415265) sdrooms< 7.173319 24 1.207754e+10 279000.00 *
## 207633) latitude< 33.74 8 5.232955e+09 301025.00 *
## 103817) sdrooms>=7.394687 10 3.878281e+09 303270.00 *
## 51909) population>=2475 12 2.688058e+10 311383.30 *
## 25955) housingMedianAge< 13.5 15 1.104881e+10 315393.30 *
## 6489) sdrooms< 6.1948 18 9.847238e+10 323350.10 *
## 3245) latitude< 33.525 13 7.549413e+10 342884.70 *
## 1623) longitude< -122.025 13 1.903161e+10 355646.20 *
## 203) housingMedianAge>=25.5 20 1.094641e+11 354510.10
## 406) longitude>=-118.29 8 4.209240e+10 310825.00 *
## 407) longitude< -118.29 12 4.192653e+10 383633.50 *
## 51) sdbedrooms>=1.064233 176 1.501459e+12 320545.60
## 102) latitude>=37.96 21 1.132533e+11 248766.70
## 204) longitude>=-122.395 14 4.919382e+10 212650.00 *
## 205) longitude< -122.395 7 9.274080e+09 321000.00 *
## 103) latitude< 37.96 155 1.265350e+12 330270.40
## 206) longitude>=-122.025 142 1.097022e+12 322652.20
## 412) housingMedianAge< 24.5 128 9.161103e+11 315620.40
## 824) sdrooms>=6.450551 97 5.760010e+11 303170.20
## 1648) longitude>=-119.725 73 3.983316e+11 290934.30
## 3296) latitude>=34.37 7 5.324296e+10 223342.90 *
## 3297) latitude< 34.37 66 3.097166e+11 298103.10
## 6594) sdbedrooms>=1.168077 17 4.610390e+10 265464.70 *
## 6595) sdbedrooms< 1.168077 49 2.392203e+11 309426.60
## 13190) sdbedrooms< 1.094899 29 8.130319e+10 287003.40
## 26380) medianIncome< 6.43985 20 4.990119e+10 273105.00
## 52760) longitude>=-117.81 8 2.774598e+10 249175.00 *
## 52761) longitude< -117.81 12 1.451995e+10 289058.30 *
## 26381) medianIncome>=6.43985 9 1.895347e+10 317888.90 *
## 13191) sdbedrooms>=1.094899 20 1.221934e+11 341940.20
## 26382) sdbedrooms>=1.108069 12 5.492194e+10 315850.10 *
## 26383) sdbedrooms< 1.108069 8 4.685067e+10 381075.20 *
## 1649) longitude< -119.725 24 1.334968e+11 340387.60
## 3298) latitude>=37.25 12 4.707191e+10 305966.70 *
## 3299) latitude< 37.25 12 5.798975e+10 374808.50 *
## 825) sdrooms< 6.450551 31 2.780260e+11 354577.50
## 1650) latitude>=34.17 7 2.201478e+10 290842.90 *
## 1651) latitude< 34.17 24 2.192830e+11 373166.80
## 3302) latitude< 33.695 15 1.199204e+11 333453.40 *
## 3303) latitude>=33.695 9 3.627631e+10 439355.90 *
## 413) housingMedianAge>=24.5 14 1.167154e+11 386943.20 *
## 207) longitude< -122.025 13 7.006715e+10 413484.90 *
## 13) housingMedianAge>=27.5 773 7.597052e+12 335979.90
## 26) medianIncome< 5.58705 332 2.949810e+12 296163.90
## 52) longitude>=-118.225 115 8.053266e+11 260317.40
## 104) sdbedrooms< 1.066468 101 4.743077e+11 246491.10
## 208) sdrooms< 6.608038 91 3.063063e+11 238351.60
## 416) housingMedianAge< 36.5 69 1.589503e+11 226692.80
## 832) longitude>=-118.055 54 6.522256e+10 215783.30
## 1664) sdrooms< 6.315213 46 4.498633e+10 208856.50
## 3328) sdbedrooms>=0.9611475 38 1.996294e+10 204331.60
## 6656) population< 1342 30 1.324042e+10 198826.70
## 13312) sdbedrooms>=1.005928 12 5.751722e+09 187275.00 *
## 13313) sdbedrooms< 1.005928 18 4.819876e+09 206527.80 *
## 6657) population>=1342 8 2.404195e+09 224975.00 *
## 3329) sdbedrooms< 0.9611475 8 2.054958e+10 230350.00 *
## 1665) sdrooms>=6.315213 8 5.338209e+09 255612.50 *
## 833) longitude< -118.055 15 6.416429e+10 265966.70 *
## 417) housingMedianAge>=36.5 22 1.085604e+11 274918.20
## 834) housingMedianAge>=43.5 11 1.419860e+10 243972.70 *
## 835) housingMedianAge< 43.5 11 7.329411e+10 305863.60 *
## 209) sdrooms>=6.608038 10 1.071105e+11 320560.10 *
## 105) sdbedrooms>=1.066468 14 1.724183e+11 360064.50 *
## 53) longitude< -118.225 217 1.918399e+12 315160.90
## 106) sdrooms>=4.796987 194 1.482210e+12 306335.60
## 212) housingMedianAge< 37.5 127 8.508762e+11 288589.00
## 424) longitude>=-122.025 89 5.534093e+11 276314.60
## 848) latitude>=37.37 10 3.228610e+10 192420.00 *
## 849) latitude< 37.37 79 4.418309e+11 286934.20
## 1698) latitude>=34.175 51 2.167511e+11 268935.30
## 3396) longitude>=-118.84 26 3.766537e+10 244215.40
## 6792) sdrooms< 5.956784 13 8.482977e+09 223715.40 *
## 6793) sdrooms>=5.956784 13 1.825590e+10 264715.40 *
## 3397) longitude< -118.84 25 1.466743e+11 294644.00
## 6794) latitude>=36.705 17 6.307972e+10 270458.80 *
## 6795) latitude< 36.705 8 5.252049e+10 346037.60 *
## 1699) latitude< 34.175 28 1.784642e+11 319717.90
## 3398) longitude>=-118.37 19 9.041185e+10 292078.90 *
## 3399) longitude< -118.37 9 4.289655e+10 378066.90 *
## 425) longitude< -122.025 38 2.526534e+11 317336.90
## 850) latitude>=37.53 24 7.345052e+10 279375.00
## 1700) latitude< 37.735 16 1.067225e+10 258793.80 *
## 1701) latitude>=37.735 8 4.244606e+10 320537.50 *
## 851) latitude< 37.53 14 8.532531e+10 382414.40 *
## 213) housingMedianAge>=37.5 67 5.155198e+11 339974.70
## 426) medianIncome< 5.2084 11 4.560390e+10 262972.70 *
## 427) medianIncome>=5.2084 56 3.918819e+11 355100.10
## 854) medianIncome>=5.235 49 3.157845e+11 344314.40
## 1708) longitude>=-122.315 41 2.192815e+11 334341.50
## 3416) latitude>=34.19 26 5.888221e+10 315288.50
## 6832) longitude>=-121.925 8 1.241808e+10 294325.00 *
## 6833) longitude< -121.925 18 4.138585e+10 324605.60 *
## 3417) latitude< 34.19 15 1.346008e+11 367366.70 *
## 1709) longitude< -122.315 8 7.152652e+10 395425.40 *
## 855) medianIncome< 5.235 7 3.049506e+10 430600.40 *
## 107) sdrooms< 4.796987 23 2.936310e+11 389600.30
## 214) sdbedrooms< 1.009963 11 1.333007e+11 309891.10 *
## 215) sdbedrooms>=1.009963 12 2.637599e+10 462667.20 *
## 27) medianIncome>=5.58705 441 3.724683e+12 365954.80
## 54) sdbedrooms< 1.042381 302 2.455658e+12 350067.00
## 108) housingMedianAge< 36.5 177 1.255049e+12 324463.30
## 216) longitude>=-122.085 145 9.476644e+11 311022.80
## 432) medianIncome< 6.37015 101 5.603068e+11 292328.70
## 864) longitude>=-117.97 21 1.434968e+11 250738.10
## 1728) latitude>=33.795 14 2.820973e+10 232371.40 *
## 1729) latitude< 33.795 7 1.011190e+11 287471.60 *
## 865) longitude< -117.97 80 3.709492e+11 303246.30
## 1730) latitude>=37.345 14 3.134774e+10 249200.00 *
## 1731) latitude< 37.345 66 2.900330e+11 314710.60
## 3462) latitude>=34.185 38 1.216956e+11 300415.80
## 6924) latitude< 34.345 15 2.903099e+10 255893.30 *
## 6925) latitude>=34.345 23 4.353926e+10 329452.20
## 13850) population>=1318.5 9 9.911689e+09 301888.90 *
## 13851) population< 1318.5 14 2.239435e+10 347171.40 *
## 3463) latitude< 34.185 28 1.500342e+11 334110.80
## 6926) housingMedianAge>=34.5 17 5.265599e+10 298894.10 *
## 6927) housingMedianAge< 34.5 11 4.371075e+10 388536.50 *
## 433) medianIncome>=6.37015 44 2.710405e+11 353934.20
## 866) latitude>=34.215 23 8.115865e+10 329682.70
## 1732) sdbedrooms>=0.9778586 13 3.147636e+10 306115.40 *
## 1733) sdbedrooms< 0.9778586 10 3.307536e+10 360320.10 *
## 867) latitude< 34.215 21 1.615393e+11 380495.30
## 1734) latitude< 34.07 13 1.045083e+11 353046.20 *
## 1735) latitude>=34.07 8 3.131928e+10 425100.20 *
## 217) longitude< -122.085 32 1.624990e+11 385365.80
## 434) population< 601.5 7 3.680366e+10 327442.90 *
## 435) population>=601.5 25 9.563404e+10 401584.20
## 870) latitude>=37.615 12 4.251676e+10 371025.10 *
## 871) latitude< 37.615 13 3.156673e+10 429792.50 *
## 109) housingMedianAge>=36.5 125 9.202764e+11 386321.80
## 218) medianIncome< 6.2549 77 5.040696e+11 363014.30
## 436) population< 423 7 4.208050e+10 267657.10 *
## 437) population>=423 70 3.919730e+11 372550.10
## 874) sdrooms< 5.273673 14 8.260927e+10 330228.60 *
## 875) sdrooms>=5.273673 56 2.780193e+11 383130.40
## 1750) longitude>=-122.43 48 2.196086e+11 374589.60
## 3500) sdrooms>=5.761098 40 1.281636e+11 363077.50
## 7000) sdrooms< 6.332459 26 6.313746e+10 346400.00
## 14000) longitude>=-118.365 7 3.454379e+10 315428.60 *
## 14001) longitude< -118.365 19 1.940526e+10 357810.50 *
## 7001) sdrooms>=6.332459 14 4.436433e+10 394050.10 *
## 3501) sdrooms< 5.761098 8 5.963820e+10 432150.10 *
## 1751) longitude< -122.43 8 3.390108e+10 434375.20 *
## 219) medianIncome>=6.2549 48 3.072767e+11 423710.80
## 438) sdrooms>=5.569937 35 2.421142e+11 408800.30
## 876) longitude< -119.16 12 1.000959e+11 378916.80 *
## 877) longitude>=-119.16 23 1.257110e+11 424391.70
## 1754) longitude>=-118.33 14 5.660099e+10 386000.10 *
## 1755) longitude< -118.33 9 1.637663e+10 484111.90 *
## 439) sdrooms< 5.569937 13 3.643158e+10 463854.40 *
## 55) sdbedrooms>=1.042381 139 1.027168e+12 400473.60
## 110) sdrooms>=5.514084 117 8.132833e+11 387754.90
## 220) population< 483 17 1.825212e+11 322394.20 *
## 221) population>=483 100 5.457917e+11 398866.20
## 442) latitude>=37.74 26 1.225176e+11 366861.60
## 884) longitude>=-122.365 17 6.681915e+10 342694.10 *
## 885) longitude< -122.365 9 2.701426e+10 412511.30 *
## 443) latitude< 37.74 74 3.872854e+11 410111.00
## 886) sdbedrooms< 1.143617 63 3.102730e+11 399166.80
## 1772) medianIncome< 6.4432 44 2.226992e+11 385891.00
## 3544) latitude>=34.135 21 8.969504e+10 356157.20
## 7088) longitude>=-121.95 13 4.066751e+10 325538.50 *
## 7089) longitude< -121.95 8 1.703512e+10 405912.60 *
## 3545) latitude< 34.135 23 9.748644e+10 413039.20
## 7090) medianIncome< 5.9159 10 4.539335e+10 385530.10 *
## 7091) medianIncome>=5.9159 13 3.870441e+10 434200.10 *
## 1773) medianIncome>=6.4432 19 6.186028e+10 429910.80 *
## 887) sdbedrooms>=1.143617 11 2.624904e+10 472791.60 *
## 111) sdrooms< 5.514084 22 9.430190e+10 468114.30
## 222) medianIncome< 5.9405 11 7.646708e+10 442446.00 *
## 223) medianIncome>=5.9405 11 3.339848e+09 493782.60 *
## 7) medianIncome>=6.8874 902 6.895520e+12 424741.10
## 14) medianIncome< 7.83595 359 2.891560e+12 374274.00
## 28) housingMedianAge< 26.5 225 1.271041e+12 345481.00
## 56) longitude>=-122.035 199 1.060915e+12 338478.00
## 112) sdbedrooms< 1.052502 139 5.665505e+11 324761.90
## 224) sdbedrooms< 0.9595679 20 7.972793e+10 276545.00
## 448) population< 810.5 8 4.023064e+10 236750.00 *
## 449) population>=810.5 12 1.838206e+10 303075.00 *
## 225) sdbedrooms>=0.9595679 119 4.325105e+11 332865.60
## 450) sdrooms>=6.644801 98 2.559564e+11 324398.00
## 900) sdbedrooms>=1.033203 24 8.532132e+10 301600.00
## 1800) sdbedrooms< 1.038677 8 9.364420e+09 269750.00 *
## 1801) sdbedrooms>=1.038677 16 6.378383e+10 317525.00 *
## 901) sdbedrooms< 1.033203 74 1.541156e+11 331791.90
## 1802) longitude>=-117.87 25 4.156415e+10 311024.00
## 3604) latitude>=33.895 7 8.806137e+09 288242.90 *
## 3605) latitude< 33.895 18 2.771237e+10 319883.30 *
## 1803) longitude< -117.87 49 9.626745e+10 342387.80
## 3606) sdbedrooms< 1.018818 40 7.522948e+10 334825.00
## 7212) population< 996.5 9 4.101996e+10 308800.00 *
## 7213) population>=996.5 31 2.634409e+10 342380.60
## 14426) population>=1503.5 23 1.838096e+10 336673.90
## 28852) population< 2226 9 3.512360e+09 320766.70 *
## 28853) population>=2226 14 1.112722e+10 346900.00 *
## 14427) population< 1503.5 8 5.060609e+09 358787.50 *
## 3607) sdbedrooms>=1.018818 9 8.582120e+09 376000.00 *
## 451) sdrooms< 6.644801 21 1.367363e+11 372381.20
## 902) medianIncome< 7.38755 12 7.280474e+10 352358.50 *
## 903) medianIncome>=7.38755 9 5.270610e+10 399078.10 *
## 113) sdbedrooms>=1.052502 60 4.076329e+11 370253.50
## 226) longitude>=-117.195 7 4.820696e+10 295600.00 *
## 227) longitude< -117.195 53 3.152614e+11 380113.40
## 454) latitude>=37.205 10 2.324544e+10 337170.00 *
## 455) latitude< 37.205 43 2.692859e+11 390100.30
## 910) longitude>=-118.2 29 1.432447e+11 364517.30
## 1820) sdrooms< 7.978204 18 6.110204e+10 342366.70 *
## 1821) sdrooms>=7.978204 11 5.885910e+10 400763.80 *
## 911) longitude< -118.2 14 6.774526e+10 443093.40 *
## 57) longitude< -122.035 26 1.256696e+11 399081.00
## 114) latitude>=37.535 16 3.529189e+10 370206.20 *
## 115) latitude< 37.535 10 5.569376e+10 445280.50 *
## 29) housingMedianAge>=26.5 134 1.120776e+12 422620.50
## 58) population< 271.5 7 1.831215e+11 290200.30 *
## 59) population>=271.5 127 8.081432e+11 429919.30
## 118) latitude>=37.65 26 1.135432e+11 380257.80
## 236) longitude>=-122.245 17 4.622184e+10 352152.90 *
## 237) longitude< -122.245 9 2.852932e+10 433344.80 *
## 119) latitude< 37.65 101 6.139704e+11 442703.40
## 238) longitude>=-117.91 13 1.277362e+11 360269.50 *
## 239) longitude< -117.91 88 3.848444e+11 454881.10
## 478) sdbedrooms< 1.013413 33 2.198591e+11 426870.00
## 956) longitude>=-118.385 13 7.672598e+10 385292.40 *
## 957) longitude< -118.385 20 1.060526e+11 453895.40
## 1914) housingMedianAge< 32 7 7.218042e+10 405528.70 *
## 1915) housingMedianAge>=32 13 8.679352e+09 479939.00 *
## 479) sdbedrooms>=1.013413 55 1.235571e+11 471687.80
## 958) housingMedianAge< 34.5 22 8.182764e+10 449004.90
## 1916) population< 919.5 8 5.221263e+10 416437.60 *
## 1917) population>=919.5 14 1.628145e+10 467614.70 *
## 959) housingMedianAge>=34.5 33 2.286387e+10 486809.80
## 1918) longitude>=-118.155 7 8.368767e+09 464471.90 *
## 1919) longitude< -118.155 26 1.006183e+10 492823.80
## 3838) sdrooms< 6.402535 7 7.449909e+09 478172.00 *
## 3839) sdrooms>=6.402535 19 5.555485e+08 498221.90 *
## 15) medianIncome>=7.83595 543 2.485099e+12 458107.10
## 30) medianIncome< 9.06925 253 1.302882e+12 429200.00
## 60) housingMedianAge< 28.5 154 7.456747e+11 398782.60
## 120) sdbedrooms< 1.000681 56 2.604958e+11 367789.30
## 240) housingMedianAge< 13.5 18 1.120118e+11 342494.50 *
## 241) housingMedianAge>=13.5 38 1.315116e+11 379771.10
## 482) sdbedrooms< 0.9765694 22 8.321329e+10 360795.50
## 964) population< 883.5 8 2.625216e+10 318137.50 *
## 965) population>=883.5 14 3.408479e+10 385171.60 *
## 483) sdbedrooms>=0.9765694 16 2.948458e+10 405862.50 *
## 121) sdbedrooms>=1.000681 98 4.006475e+11 416493.10
## 242) longitude>=-117.775 21 5.368809e+10 374333.30
## 484) population< 1722 14 2.813261e+10 354471.40 *
## 485) population>=1722 7 8.986677e+09 414057.10 *
## 243) longitude< -117.775 77 2.994532e+11 427991.20
## 486) latitude>=34.165 46 1.592639e+11 408150.10
## 972) longitude>=-121.48 17 6.587210e+10 379270.60 *
## 973) longitude< -121.48 29 7.090193e+10 425079.40
## 1946) longitude< -121.885 22 5.288334e+10 416122.90
## 3892) sdbedrooms>=1.028967 13 2.373019e+10 398946.20 *
## 3893) sdbedrooms< 1.028967 9 1.977754e+10 440933.60 *
## 1947) longitude>=-121.885 7 1.070707e+10 453228.70 *
## 487) latitude< 34.165 31 9.520950e+10 457432.80
## 974) longitude>=-118.035 12 4.573682e+10 420725.20 *
## 975) longitude< -118.035 19 2.309113e+10 480616.50 *
## 61) housingMedianAge>=28.5 99 1.930839e+11 476515.80
## 122) latitude>=37.805 21 5.081058e+10 441309.80
## 244) sdbedrooms< 1.040328 14 2.681605e+10 426221.50 *
## 245) sdbedrooms>=1.040328 7 1.443293e+10 471486.40 *
## 123) latitude< 37.805 78 1.092368e+11 485994.40
## 246) sdbedrooms< 1.032476 38 9.200232e+10 475245.40
## 492) housingMedianAge< 35.5 15 6.789445e+10 452233.70 *
## 493) housingMedianAge>=35.5 23 1.098461e+10 490253.00
## 986) housingMedianAge>=43.5 10 8.462838e+09 478500.60 *
## 987) housingMedianAge< 43.5 13 7.814622e+07 499293.20 *
## 247) sdbedrooms>=1.032476 40 8.672932e+09 496205.90 *
## 31) medianIncome>=9.06925 290 7.863664e+11 483326.00
## 62) population< 134.5 13 2.333986e+11 355369.60 *
## 63) population>=134.5 277 3.301317e+11 489331.20
## 126) housingMedianAge< 18.5 68 2.054327e+11 469400.60
## 252) medianIncome< 10.6756 35 1.576969e+11 449177.50
## 504) population< 1932 25 1.329800e+11 433624.30
## 1008) population>=985 12 9.181791e+10 403150.20 *
## 1009) population< 985 13 1.973125e+10 461754.20 *
## 505) population>=1932 10 3.550387e+09 488060.60 *
## 253) medianIncome>=10.6756 33 1.824030e+10 490849.30
## 506) population< 691 10 1.241136e+10 477590.60 *
## 507) population>=691 23 3.306702e+09 496613.90 *
## 127) housingMedianAge>=18.5 209 8.889902e+10 495815.80
## 254) sdrooms< 6.250908 7 3.967099e+10 442014.90 *
## 255) sdrooms>=6.250908 202 2.826412e+10 497680.20
## 510) longitude>=-117.925 26 1.392379e+10 490220.00
## 1020) latitude>=33.785 7 7.915247e+09 465500.40 *
## 1021) latitude< 33.785 19 1.552411e+08 499327.30 *
## 511) longitude< -117.925 176 1.267958e+10 498782.20 *##
## Call:
## randomForest(formula = medianHouseValue ~ longitude + latitude + housingMedianAge + sdrooms + sdbedrooms + population + medianIncome, data = cahousing_train, importance = TRUE)
## Type of random forest: regression
## Number of trees: 500
## No. of variables tried at each split: 2
##
## Mean of squared residuals: 2764225973
## % Var explained: 79.41## Distribution not specified, assuming gaussian ...## gbm(formula = medianHouseValue ~ longitude + latitude + housingMedianAge +
## sdrooms + sdbedrooms + population + medianIncome, data = cahousing_train)
## A gradient boosted model with gaussian loss function.
## 100 iterations were performed.
## There were 7 predictors of which 6 had non-zero influence.Now, we estimate their RMSE to find out which model is our best predictive model.
## [1] 72148.38## [1] 68103.15## [1] 61142.87## [1] 49765.22## [1] 71622.62According to our results, we can find the Random Forecast model has lower RMSE, so we use this to build our best predictive model.
We can find that above graphs are perform well, because Figure1: Actual Median House Value in California are almost match with Figure 4-2: Prediction Value in California. Therefore, we can indicate the random forest is the best predictive model in this case. In conclusion, our predictive model is effective, then we may use this predictive model to forecast other states or area in United State.